The present invention relates to an improved technique for forming a holographic stereo gram.
A hologram is a device that can produce a three dimensional image of an object. In order to produce a hologram, an object is illuminated by a laser in an optical set up. Light reflected off the object is combined with a reference beam on the surface of a photographic plate. The interference pattern between these two light beams is recorded to form the hologram. This process of making a hologram requires an actual object and precise optical arrangement between the object and the reference beam to produce the interference fringes. However, the human brain can combine views perceived by the right and left eyes to produce a perception of a three dimensional object. The two dimensional views can be photographs of an object or views of an object created by a computer.
A stereogram is a pair of pictures presenting two different views of an object. The three dimensional image produced by a stereogram typically has only horizontal parallax. There are many methods of presenting views of an object to the right and left eyes separately. The most common one is using a stereo viewer, which simply restricts the right eye to see one view and the left eye to see the other view of an object. Stereograms can also be printed in red and green color. By means of using color filter in front of the right and left eye, each eye will see different views of the object. Examples of stereograms can be found in U.S. Pat. Nos. 6,037,971 and 5,795,154.
One type of stereogram is called a lenticular stereogram. This is one of a number of methods for viewing stereo grams without the use of a viewing aid. The lenticular stereogram technique interlaces narrow strips of the two views and placed them behind a set of prisms so that alternate segments of the two views are separately projected to the right and left eyes.
A holographic stereogram is another method whereby two images are encoded with different spatial frequency so that when the hologram is illuminated by light, the two images will emerge from the hologram at different angles. The diffraction angle is determined by the separation of the eyes and the viewing distance. For a typical eye separation of 50 mm and a viewing distance of 400 mm, the angle is about 7.5 degrees.
FIG. 1 shows light beam 102 as bounded by ray 102a and ray 102b and beam 103 as bounded by ray 103a and ray 103b diffracted from the holographic stereogram 101 toward the right eye 104 and left eye 105. Ray 102a and ray 103a are emitted from hologram element 106 in the holographic stereogram 101. This suggests a technique for constructing such a holographic stereogram with only horizontal parallax by constructing the stereogram by having two beams such as 102a and 103a interfering within a narrow slit and composing the stereograms one narrow segment at a time. See Mark Holzbach, “Three dimensional image processing for synthetic holographic stereograms”, M.S. thesis. Massachusetts Institute of Technology, September 1986, pp. 1 86; C. K. Lee et al., “Optical configuration and color-representation of a variable-pitch dot matrix holographic printer” Appl. Opt., Vol. 39, No. 1, p. 40 (2000); U.S. Pat. Nos. 5,237,433, 5,475,511 and 5,793,503.
FIG. 2(a) shows how the hologram of FIG. 1 is formed. A converging cone of laser light 201 illuminates a transparency 202 (which could be an LCD display). An image of the transparency is projected on a rotating diffuser 205, which produces uniform illumination at the recording plane 207. To record a stereogram the image segment 204 corresponds to the image for the left eye and the image segment 203 corresponds to the image for the right eye. The diffused light from these two image segments propagates to the recording plane 207. A reference laser beam 206 is introduced to interfere with the light from the diffuser and produce interference fringes on a hologram recording area 209 of the recording plane 207. Slit 208 confines the hologram recording to a narrow stripe. The width of the slit determines the image resolution of the hologram plane. After one hologram stripe has been recorded, the recording plane is moved to the next position and a new set of images is projected on the diffuser for the next recording. This process is repeated until the recording surface 207 as shown in FIG. 2(b) is filled with a holographic stereogram. This is a simple process to record a pair of stereo images in the same hologram. When this hologram is illuminated by light, the eyes positioned at location near the diffuser will see a stereo image of the recorded object as shown in FIG. 1. The diffuser 203 in FIG. 1 can also replaced by a cylindrical lens, which focuses the laser beam into a line with a width matching the width of slit 208 as shown in FIG. 3(a).
FIG. 3 further extends the concept illustrated in FIG. 2. Instead of recording just a stereo pair, the film 302 contains many views of the object illuminated similarly by a converging cone of laser light. All these views on film are combined into the same hologram unit 309. Pixels 303, 304 are two of these images corresponding to certain views of the object. FIG. 3(b) shows the process of constructing such views. Layers 311, 312 represent two-dimensional images of certain views of the object. View images are stacked together to form a cube 310. On the front side of this cube, stripes 313, 314 are image units in certain locations in a view such as 311 or any other view. To properly record the hologram unit j which corresponds to image location x=j, the view recorded on film is g(z=nδ, y, x=j) where j indicates location on the x-y plane and n indicates the view frame and δ is the width of stripes such as 310 or 312. Mathematically, the light distribution on the focal plane of the cylindrical lens can be written as:
                              G          ⁡                      (                                          u                -                                  j                  ⁢                                                                          ⁢                  Δ                                            ,              y                        )                          =                              ∑                          n              =                                                -                  M                                /                2                                                    M              /              2                                ⁢                                          ⁢                                    g              ⁡                              (                                  n                  ,                  y                  ,                  j                                )                                      ⁢                          ⅇ                                                j                  ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                  n                  ⁢                                                                          ⁢                  δ                  ⁢                                                                          ⁢                  u                                                  λ                  ⁢                                                                          ⁢                  F                                                                                        (        1        )            where G(u−jΔ, y) is the light distribution on the recording plane. As can be seen, the image segment g(z=nδ, y, x=j) is incident on the hologram with an angle given by sin θn=nδ/λF. When such hologram is recorded, the eye will see a gradual change of the views of the object as the eyes scan through the stereogram. See Mark Holzbach, “Three dimensional image processing for synthetic holographic stereograms”, M.S. thesis. Massachusetts Institute of Technology, September 1986, pp. 1 86. From a practical point of view, the width of a hologram unit Δ determines the resolution of the stereo image reproduced by this holographic stereogram. It is the objective of this present invention to describe a technique whereby each hologram unit contains more than one image pixel.